Method and apparatus for efficiently performing discrete monte carlo simulation analysis in network-based microservices

ABSTRACT

Aspects of the subject disclosure may include, for example, receiving from a database server via a network, a reduced size set of quantile samples of a plurality of variables associated with a dynamic system, wherein the reduced size set of quantile samples is based on a standard set of quantile samples, wherein the standard set of quantile samples comprises M quantile samples based on dividing each distribution of the plurality of variables into 1/M probability steps, and wherein the reduced size set of quantile samples comprises N quantile samples based on dividing each distribution of the plurality of variables into 1/N probability steps, performing a plurality of linear interpolations upon the reduced size set of quantile samples to a restored size set of quantile samples, performing a Monte Carlo simulation using the restored size set of quantile samples to generate a simulation result, and transmitting the simulation result to a client device. Other embodiments are disclosed.

FIELD OF THE DISCLOSURE

The subject disclosure relates to a method and apparatus for efficiently performing discrete Monte Carlo simulation analysis in network-based microservices.

BACKGROUND

Modern telecommunications systems provide consumers with telephony capabilities while accessing a large variety of content. Consumers are no longer bound to specific locations when communicating with others or when enjoying multimedia content or accessing the varied resources available via the Internet. Network capabilities have expanded and have created additional interconnections and new opportunities for using mobile communication devices in a variety of situations. Intelligent devices offer new means for experiencing network interactions in ways that anticipate consumer desires and provide solutions to problems.

BRIEF DESCRIPTION OF THE DRAWINGS

Reference will now be made to the accompanying drawings, which are not necessarily drawn to scale, and wherein:

FIG. 1 is a block diagram illustrating an exemplary, non-limiting embodiment of a communications network in accordance with various aspects described herein.

FIG. 2A is a block diagram illustrating an example, non-limiting embodiment of a system functioning within the communication network of FIG. 1 to provide a Monte Carlo simulation via a web microservice in accordance with various aspects described herein.

FIG. 2B is a workflow diagram illustrating an example, non-limiting embodiment of a system functioning within the communication network of FIG. 1 to provide a Monte Carlo simulation via a web microservice in accordance with various aspects described herein.

FIG. 2C is a graph illustrating an example, non-limiting embodiment of reducing Monte Carlo simulation service response time while minimizing service degradation in accordance with various aspects described herein.

FIG. 2D is a graph illustrating an example, non-limiting embodiment of reducing Monte Carlo simulation service response time while minimizing service degradation in accordance with various aspects described herein.

FIG. 2E depicts an illustrative embodiment of a method in accordance with various aspects described herein.

FIG. 3 is a block diagram illustrating an example, non-limiting embodiment of a virtualized communication network in accordance with various aspects described herein.

FIG. 4 is a block diagram of an example, non-limiting embodiment of a computing environment in accordance with various aspects described herein.

FIG. 5 is a block diagram of an example, non-limiting embodiment of a mobile network platform in accordance with various aspects described herein.

FIG. 6 is a block diagram of an example, non-limiting embodiment of a communication device in accordance with various aspects described herein.

DETAILED DESCRIPTION

The subject disclosure describes, among other things, illustrative embodiments for providing a Monte Carlo simulation via a microservice. A request for a Monte Carlo simulation of a dynamic system can be received. A request for quantile samples for variables of the dynamic system can be sent to database server. A reduce-size set of quantile samples can be received from the database server over a network. A standard set of M quantile samples, which divides the variables into 1/M probability steps, can be converted to a reduced sized set of N quantile samples, which divide the variables into 1/N probability steps. By sending a reduced size set of quantile samples from the database server the network demands are decreased, and the speed is increased. Interpolation can be performed on the reduced size set of quantile samples to generate a restored size set of quantile samples. The Monte Carlo simulation can be performed on the restored size set of quantile samples and the results can be reported to a requesting client device. Other embodiments are described in the subject disclosure.

One or more aspects of the subject disclosure a method performed by a processing system including a processor. The method can include receiving a first request from a client device for a Monte Carlo simulation of a dynamic system, and, in turn, transmitting a second request to a database server for quantile samples of a plurality of variables associated with the dynamic system responsive to the receiving the first request. The method can also include receiving, from the database server via the network, a reduced size set of quantile samples of the plurality of variables associated with the dynamic system. The reduced size set of quantile samples of the plurality of variables can be based on a standard set of quantile samples of the plurality of variables associated with the dynamic system. The standard set of quantile samples can comprise M quantile samples based on dividing each distribution of the plurality of variables into 1/M probability steps. The reduced size set of quantile samples can comprise N quantile samples based on dividing each distribution of the plurality of variables into 1/N probability steps. A third set of quantile samples of a first variable of the plurality of variables can be added to the reduced size set of quantile samples according to the first variable being unbounded. The method can further include performing a plurality of linear interpolations upon the reduced size set of quantile samples of the plurality of variables associated with the dynamic system to generate a restored size set of quantile samples of the plurality of variables associated with the dynamic system. The method can provide performing the Monte Carlo simulation using the restored size set of quantile samples of the plurality of variables associated with the dynamic system to generate a simulation result, and, in turn, transmitting the simulation result to the client device.

One or more aspects of the subject disclosure include a device, including a processing system including a processor and a memory that stores executable instructions that, when executed by the processing system, facilitate performance of operations. The operations can include transmitting, via a network, a request to a database server for quantile samples of a plurality of variables associated with a dynamic system. The operations can also include receiving from the database server via the network, a reduced size set of quantile samples of the plurality of variables associated with the dynamic system. The reduced size set of quantile samples of the plurality of variables can be based on a standard set of quantile samples of the plurality of variables associated with the dynamic system. The standard set of quantile samples can comprise M quantile samples based on dividing each distribution of the plurality of variables into 1/M probability steps. The reduced size set of quantile samples can comprise N quantile samples based on dividing each distribution of the plurality of variables into 1/N probability steps. The operations can further include performing a plurality of linear interpolations upon the reduced size set of quantile samples of the plurality of variables associated with the dynamic system to generate a restored size set of quantile samples of the plurality of variables associated with the dynamic system. The operations can include performing a Monte Carlo simulation using the restored size set of quantile samples of the plurality of variables associated with the dynamic system to generate a simulation result, and, in turn, transmitting the simulation result to a client device.

One or more aspects of the subject disclosure include a non-transitory machine-readable medium, comprising executable instructions that, when executed by a processing system including a processor, facilitate performance of operations. The operations can include receiving from a database server via a network, a reduced size set of quantile samples of a plurality of variables associated with a dynamic system. The reduced size set of quantile samples of the plurality of variables can be based on a standard set of quantile samples of the plurality of variables associated with the dynamic system. The standard set of quantile samples can comprise M quantile samples based on dividing each distribution of the plurality of variables into 1/M probability steps. The reduced size set of quantile samples can comprise N quantile samples based on dividing each distribution of the plurality of variables into 1/N probability steps. The operations can also include performing a plurality of linear interpolations upon the reduced size set of quantile samples of the plurality of variables associated with the dynamic system to generate a restored size set of quantile samples of the plurality of variables associated with the dynamic system. The operations can further include performing a Monte Carlo simulation using the restored size set of quantile samples of the plurality of variables associated with the dynamic system to generate a simulation result, and, in turn, transmitting the simulation result to a client device.

Referring now to FIG. 1, a block diagram is shown illustrating an example, non-limiting embodiment of a system 100 in accordance with various aspects described herein. For example, system 100 can facilitate, in whole or in part, providing a Monte Carlo simulation via a microservice. A request for a Monte Carlo simulation of a dynamic system can be received. A request for quantile samples for variables of the dynamic system can be sent to database server. A reduce-size set of quantile samples can be received from the database server over a network. A standard set of M quantile samples, which divides the variables into 1/M probability steps, can be converted to a reduced sized set of N quantile samples, which divide the variables into 1/N probability steps. By sending a reduced size set of quantile samples from the database server the network demands are decreased, and the speed is increased. Interpolation can be performed on the reduced size set of quantile samples to generate a restored size set of quantile samples. The Monte Carlo simulation can be performed on the restored size set of quantile samples and the results can be reported to a requesting client device.

In particular, a communications network 125 is presented for providing broadband access 110 to a plurality of data terminals 114 via access terminal 112, wireless access 120 to a plurality of mobile devices 124 and vehicle 126 via base station or access point 122, voice access 130 to a plurality of telephony devices 134, via switching device 132 and/or media access 140 to a plurality of audio/video display devices 144 via media terminal 142. In addition, communication network 125 is coupled to one or more content sources 175 of audio, video, graphics, text and/or other media. While broadband access 110, wireless access 120, voice access 130 and media access 140 are shown separately, one or more of these forms of access can be combined to provide multiple access services to a single client device (e.g., mobile devices 124 can receive media content via media terminal 142, data terminal 114 can be provided voice access via switching device 132, and so on).

The communications network 125 includes a plurality of network elements (NE) 150, 152, 154, 156, etc. for facilitating the broadband access 110, wireless access 120, voice access 130, media access 140 and/or the distribution of content from content sources 175. The communications network 125 can include a circuit switched or packet switched network, a voice over Internet protocol (VoIP) network, Internet protocol (IP) network, a cable network, a passive or active optical network, a 4G, 5G, or higher generation wireless access network, WIMAX network, UltraWideband network, personal area network or other wireless access network, a broadcast satellite network and/or other communications network.

In various embodiments, the access terminal 112 can include a digital subscriber line access multiplexer (DSLAM), cable modem termination system (CMTS), optical line terminal (OLT) and/or other access terminal. The data terminals 114 can include personal computers, laptop computers, netbook computers, tablets or other computing devices along with digital subscriber line (DSL) modems, data over coax service interface specification (DOCSIS) modems or other cable modems, a wireless modem such as a 4G, 5G, or higher generation modem, an optical modem and/or other access devices.

In various embodiments, the base station or access point 122 can include a 4G, 5G, or higher generation base station, an access point that operates via an 802.11 standard such as 802.11n, 802.11ac or other wireless access terminal. The mobile devices 124 can include mobile phones, e-readers, tablets, phablets, wireless modems, and/or other mobile computing devices.

In various embodiments, the switching device 132 can include a private branch exchange or central office switch, a media services gateway, VoIP gateway or other gateway device and/or other switching device. The telephony devices 134 can include traditional telephones (with or without a terminal adapter), VoIP telephones and/or other telephony devices.

In various embodiments, the media terminal 142 can include a cable head-end or other TV head-end, a satellite receiver, gateway or other media terminal 142. The display devices 144 can include televisions with or without a set top box, personal computers and/or other display devices.

In various embodiments, the content sources 175 include broadcast television and radio sources, video on demand platforms and streaming video and audio services platforms, one or more content data networks, data servers, web servers and other content servers, and/or other sources of media.

In various embodiments, the communications network 125 can include wired, optical and/or wireless links and the network elements 150, 152, 154, 156, etc. can include service switching points, signal transfer points, service control points, network gateways, media distribution hubs, servers, firewalls, routers, edge devices, switches and other network nodes for routing and controlling communications traffic over wired, optical and wireless links as part of the Internet and other public networks as well as one or more private networks, for managing subscriber access, for billing and network management and for supporting other network functions.

FIG. 2A is a block diagram illustrating an example, non-limiting embodiment of a system 200 functioning within the communication network of FIG. 1 to provide a Monte Carlo simulation via a web microservice in accordance with various aspects described herein. In one or more embodiments, the system 200 can include a web micro service server 230 and client devices 210. The web micro service server 230 can provide Monte Carlo simulation services for client devices 210. The system 200 can include a database server 220. The web micro service server 230 can access the database server 220 for sets of quantile samples of variables for use in Monte Carlo simulations. The system 200 can include a pre-calculation server 225. The pre-calculation server can provide reduced size quantile samples to the database server 220. The web micro service server 230 can be coupled to client devices 210 and to the database server 220 via a communications network 250.

In one or more embodiments, a client device 210 can send a request to the web micro services server 230 over the communications network 250. For example, the client device 210 can request that the web micro service server 230 perform a Monte Carlo simulation on a dynamic system. Generally, a Monte Carlo simulation analysis can model the probability of different outcomes in a dynamic system by using repeated random sampling of system variables to calculate numerical results or predictions of the system behavior. Monte Carlo analysis can relies on large numbers of random samples of variables, which are used to simulate the system a large number of times.

In one or more embodiments, in a micro services environment, responsiveness of the service, such as the provision of Monte Carlo simulations, can be improved by reducing the amount of data—in this case, quantiles samples for the various variables—being queried and passed over the communications network 250. Conversely, excessive amounts of data can slow down the responsiveness of the service. In some situations, prompt response can be critical. In one embodiment, the data volume necessary for performing a discrete Monte Carlo simulation can be reduced by 80-90% without significant degradation to the quality of analysis.

In one or more embodiments, when performing a Monte Carlo simulation analysis of a continuous random variable with enough samples and without assuming its theoretical distribution, an inverse empirical cumulative distribution function (a.k.a. quantile) samples can be pre-calculated. The quantile samples can have a 1/M step increase in probability between 0 and 1. For example, if M=1000, then a quantiles samples set can be calculated for with quantiles [0.000, 0.001, 0.002, . . . , 0.999, 1.000]. This set of quantile samples can be used for performing a discrete Monte Carlo simulation analysis. Generally, the larger the number M (e.g., from 1000 to 10,000), then the more accurate the analysis. However, this added accuracy can carry with it the drawback of added data volume. In a micro service environment, these quantile samples are usually stored in a database server 220 and are access over a communications network 250. Therefore, a large volume of data must be queried and retrieved over the communications network 250. In many cases, this data can be in text format (e.g., JSON). Generally, greater data volume can result in slower the service response. In situations, such as complex dynamic systems, where many random variables are involved, the increase response time for the Monte Carlo analysis with M quantiles may be prohibitively expensive. Conversely, reducing the required data volume for the Monte Carlo analysis can reduce response time and expenses. This reduction can be very useful as long as there is minimal impact on the quality of analysis.

In one or more embodiments, a Monte Carlo simulation can include a desired sample accuracy parameter, M. The 1/M probability step can be used for calculating quantile samples in a normal (traditional) approach. For example, if M=1000, then the quantiles for the Monte Carlo simulations can be quantile(q), q=0.000, 0.001, 0.002, . . . , 0.999, 1.000. A reduced size sampling accuracy parameter, N, can be used for calculating a reduced number of quantile samples. N can be chosen according to N=int(M/10), where 1/N can be the probability step in calculating quantile samples in for the reduced size sampling. For example, where M=1000, then N can be int(1000/10), or N=100. By selecting N=100, the quantiles for the Monte Carlo simulations can be quantile(q), q=0.00, 0.01, 0.02, . . . , 0.99, 1.00. As can be seen, N=100 results in a 90% reduction in the number of quantile samples. If bandwidth of the communications network 250 is the bottleneck in performing the Monte Carlo analysis, then reducing the data transfer from the database server 220 to the web micro service server 230 by 90% can result in substantial savings of time and/or expense. In one or more embodiments, the pre-calculation server 225 can pre-calculate the reduced size set of quantile samples N from the standard set of quantile sample M and store these at the database server 220.

In one or more embodiments, the random variables of the dynamic system that is subject to Monte Carlo simulation can be categorized according to how the values of these variables behave at the boundaries of their ranges of values. If a random variable operates within a predictable upper and lower range of values, then it can be described as a bounded variable. The probability distribution of a bounded variable can behave in a predictable manner, such that translation from 1/M probability steps to 1/N probability steps in the reduced size set of quantile samples can, likewise, yield predictable results with minimal degradation of simulation accuracy. However, some random variables may not have predicable upper and/or lower boundaries. In these cases, the variables can be described as either minimum unbounded or maximum unbounded (or both). In a minimum unbounded variable, the minimum value of the random variable may have no definite boundary. In the maximum unbounded variable, the maximum value of the random variable may have no definite boundary.

In one or more embodiments, to compensate for unbounded variables, additional 1/M type quantile samples can be added to the set of quantile samples for this variable in the value region that is unbounded. For a minimum unbounded variable, E1 quantile samples of the 1/M type can be added to the reduced sized (1/N type) set of quantile samples. These E1 additional 1/M quantile samples can be added after the q=0 quantile sample. Similarly, for a maximum unbounded variable, E2 quantile samples of the 1/M type can be added to the reduced sized (1/N type) set of quantile samples. These E2 additional 1/M quantile samples can be added before the q=1 quantile sample. The number of additional samples E1 and E2 that can be added for the unbounded variables can be chosen such that E1+E2 is less than or equal to M. Generally, E1 or E2 can be chosen as much less than (orders of magnitude less than) M. However, if E1+E2 is chosen as equally M, then the processing method reverts back to all the quantile samples being 1/M, and there is no reduction in the volume of data in the set of quantile samples.

In one or more embodiments, the pre-calculation server 225 generates the reduced size set of quantile samples q according to the above-described translation from M quantile samples of 1/M type to N quantile samples of 1/N type, where quantile q=n/N, for n=0, 1, 2, . . . , N−1, N. The pre-calculation server 225 can add E1 and/or E2 additional 1/M samples to either or both ends of the reduced size set of quantile samples for random variables that are minimum unbounded or maximum unbounded, respectively. For minimum unbounded random variables, the pre-calculation server 225 can add quantile q, where q=e/M, for e=1, 2, . . . E1. For minimum unbounded random variables, the pre-calculation server 225 can add quantile q, where q=(M−e)/M, for e=1, 2, . . . E2. The original or 1/M type quantile samples can be stored and accessed by the pre-calculation server 225 at the database server 220. The reduced size set of (1/N type) quantile samples can be stored at the database server 220.

In one example, a set of random variables for a dynamic system can have M=1000 and N=100 (using N=int(M/10). To account for the minimum unbounded and maximum unbounded variables, additional quantile samples can be added using E1=5 and E2=5. In this example, the pre-calculation server 225 can pre-calculate 1/N type quantile samples q to create a set of quantile samples q=0.00, 0.01, . . . , 0.99, 1.00. The pre-calculation server 225 can pre-calculate E1=5 additional 1/M quantile samples for the minimum unbounded variables and add them after the q=0.00 quantile as q=(0.001, 0.002, 0.0003, 0.004, 0.005). The pre-calculation server 225 can pre-calculate E2=5 additional 1/M quantile samples for the maximum unbounded variables and add them prior to the q=1.00 quantile as q=(0.995, 0.996, 0.997, 0.998, 0.999).

In one or more embodiments, the web micro service server 230 can send a quantile sample request to the database server 220. In response to the request, the database server 220 can send the reduced size set of quantile samples from the database server 220. After web micro service server 230 retrieves the pre-calculated reduced size set of quantile samples from database server, the web micro service server 230 can restore the 1/N type quantile samples to 1/M type samples. The web micro service server 230 can perform linear interpolation calculations on the reduced size set of quantile samples to generate the “missing” 1/M type samples that were removed by the pre-calculation server 225 while transforming from 1/M type samples to 1/N type samples. The purpose of the interpolation step is to transform the reduced size set of quantile samples of 1/N type having the form of, for example, q=0.00, 0.01, . . . , 0.99, 1.00 to a restored set of quantile samples of 1/M type having the form of, for example, q=0.000, 0.001, 0.002, . . . , 0.999, 1.000. This means that, for those 1/M quantiles not already included in the reduced size set of quantile samples, these “missing” samples are inferentially generated using linear interpolations based on the available samples in the reduced size set. In one or more embodiments, the web micro service server 230 can generate the additional 1/M type quantile samples by linear interpolation according to S_(m)=interp(q_(m), q_(r), S_(r)), where interp is a linear interpolation, where q vector q_(m)=n/M, n=[0, 1, . . . , M], where q_(r)=q vector used to pre-calculated the quantile samples, and where S_(r)=calculated quantile samples retrieved.

In one or more embodiments, the web micro service server 230 can perform the Monte Carlo simulation using the restored size set of quantile samples. The Monte Carlo simulation can provide a set of simulation results which have reasonable accuracy, when compared to a similar simulation run with the entire, original 1/M type set of quantile samples. However, the reduced size set of quantile samples that are used in this method can be accessed by the web micro service server 230 with greater speed and less expense. The web micro service server 230 can send the analytic service response from the Monte Carlo simulation to the client device 210 via the communications network 250.

In one or more embodiments, by accessing the reduced-size quantile samples for the Monte Carlo simulation, the web micro service server 230 can increase the efficiency of the simulation when compared to performing a Monte Carlo simulation by downloading the entire standard-sized quantile samples from the database server 220. This increase in efficiency can be in the form of reduced time for providing the sample results to the client device 210, reduced demands upon the communications network 250, and/or reduced cost.

FIG. 2B is a workflow diagram illustrating an example, non-limiting embodiment of a system functioning within the communication network of FIG. 1 to provide a Monte Carlo simulation via a web microservice in accordance with various aspects described herein. In the workflow diagram 262, at step 0.1, the pre-calculation server can calculate the quantile samples for the reduced size set of quantile samples. In step 0.2, the pre-calculation server can store the calculated quantile samples to the data storage server. In step 1, a user can send a request for a Monte Carlo simulation to the web micro service. In step 2, the web micro service can send a quantile sample request to the database server. In step 3, the database server can send back quantile samples with reduced response time due to reduced data volume. In step 4, the web micro service server can perform the interpolation of the reduced size set of quantile samples to generate the restored size set of quantile samples. The web micro service server can perform the Monte Carlo simulation on the restored size set of quantile samples. In step 5, the web micro service server can report the results of the Monte Carlo simulation with reduced response time.

In one or more embodiments, the web micro service server 230 can request a full size set of quantile samples instead of the reduced size set of quantile samples. For example, if the client device 210 requests the Monte Carlo simulation during times of low usage of the communications network 250, then the web micro service server 230 can conclude that the tradeoff in response time due to the larger amount of data obtained from the database server is minimal due to the timing of the request. This situation can occur during non-peak hours or other times when the communications network 250 has additional capacity or bandwidth. The decision to send the full size set of quantile samples can be made by automatically by detecting low usage/excess bandwidth in the communications network 250. Alternatively, the client device 210 can request that the simulation be performed with the full size set of quantile samples.

In one or more embodiments, preprocessing the input data used in the Monte Carlo analysis can result in reduced web service response time, in exchange for some degradation of analysis quality. The extent of the service time reduction can be a function of a multitude of factors including the capacity of the web micro service server 230, the capacity of the database server 220, the network bandwidth of the communications network 250, the total number of random variables in the dynamic system, the number of minimum unbounded and maximum unbounded variables, and the M, N, E1, and E2 parameters. It is found that the service response time can be reduced by up to 90% for situations, where the delay bottleneck is primarily due to the time required for accessing the data from the database server and where the data processing time is proportional to data volume.

In one or more embodiments, it is found that a major contributing factor to degradation of the quality of the resulting Monte Carlo analysis can be the shape of the inverse cumulative distribution function (CDF) of the random variables. It is found that the steepness of the inverse CDF at the boundaries can degrade the quality of the Monte Carlo analysis using the reduced-then-restored set of quantile samples. It is also found that the E1 and E2 parameters can significantly affect the quality of the analysis. For a minimum or maximum unbounded variable having an inverse CDF with a steep curve, degradation may be controlled by proper choices for the E1 or E2 value. Conversely, if to variable has a uniform distribution, then it is found that there is no degradation using this approach. For the special case where E1=E2=M/2, the resulting reduced size set of quantile samples is, in fact, not reduced at all. There is no analysis quality degradation and no response time reduction.

FIG. 2C is a graph illustrating an example, non-limiting embodiment of reducing Monte Carlo simulation service response time while minimizing service degradation in accordance with various aspects described herein. The graph 260 illustrates how the approach to Monte Carlo simulation trades off service response improvement and quality degradation. Assuming the existence of a slow, bottlenecked database server and that the pre-processing time is proportional to the volume of data requested, the maximum response time reduction using the approach is found to be

R _(max)=0.90(M−E1−E2)/M

R _(max)=0.90(M−T)/M, where T=(E1+E2).

It is found that the maximum service degradation D_(max) is a function of the cumulative distribution functions (CDF_(i)) of all the random variables i (i=1 to K) for the dynamic system as well as (E1, E2). It is found that D_(max) decreases over E1 and E2 with non-uniform variables. Also, it is found that D_(max)=0 for random variables with uniform distributions. Further, it is found that, where at least one of the E1 or E2 is zero or where E1=E2, then it can be deduced that D_(max)=f (CDF_(i), T) and decreases over T=(E1+E2).

FIG. 2D is a graph illustrating an example, non-limiting embodiment of reducing Monte Carlo simulation service response time while minimizing service degradation in accordance with various aspects described herein. The graph 265 illustrates sample device speed using the reduced size quantile samples in Monte Carlo simulations via a device speed simulation analysis. The device speed variable can be characterized as maximum unbounded with a steep curve. Using parameters of M=1000, N=100, and E2=5, it was found that the approach improved service response speed by 25%, while the degradation of the quality of the analysis was less than 2% (as measured by average difference of mean and median of resulting the Monte Carlo simulation samples). By contrast, if E2=0, then the degradation of the quality of the analysis was 11%, while the service response speed improvement was 26%.

FIG. 2E depicts an illustrative embodiment of a method in accordance with various aspects described herein. In the method 270, a request for a Monte Carlo simulation of a dynamic system can be received from a client device at step 272. At step 274, a request is transmitted to a database server for a set of quantile samples of variables for the dynamic system. At step 276, a reduced size set of quantile samples of the variables can be received from the database server. At step 278, a linear interpolation process is performed on the reduced size set of quantile samples to generate a restored size set of quantile samples. At step 280, the Monte Carlo simulation is performed on the restored size set of quantile samples to generate the simulation result for the dynamic system. At step 282, the simulation result is transmitted to the client device.

While for purposes of simplicity of explanation, the respective processes are shown and described as a series of blocks in FIG. 2X, it is to be understood and appreciated that the claimed subject matter is not limited by the order of the blocks, as some blocks may occur in different orders and/or concurrently with other blocks from what is depicted and described herein. Moreover, not all illustrated blocks may be required to implement the methods described herein.

Referring now to FIG. 3, a block diagram 300 is shown illustrating an example, non-limiting embodiment of a virtualized communication network in accordance with various aspects described herein. In particular a virtualized communication network is presented that can be used to implement some or all of the subsystems and functions of system 100, the subsystems and functions of system 200, and method 230 presented in FIGS. 1, 2A, 2B, 2C, and 3. For example, virtualized communication network 300 can facilitate, in whole or in part, providing a Monte Carlo simulation via a microservice. A request for a Monte Carlo simulation of a dynamic system can be received. A request for quantile samples for variables of the dynamic system can be sent to database server. A reduce-size set of quantile samples can be received from the database server over a network. A standard set of M quantile samples, which divides the variables into 1/M probability steps, can be converted to a reduced sized set of N quantile samples, which divide the variables into 1/N probability steps. By sending a reduced size set of quantile samples from the database server the network demands are decreased, and the speed is increased. Interpolation can be performed on the reduced size set of quantile samples to generate a restored size set of quantile samples. The Monte Carlo simulation can be performed on the restored size set of quantile samples and the results can be reported to a requesting client device.

In particular, a cloud networking architecture is shown that leverages cloud technologies and supports rapid innovation and scalability via a transport layer 350, a virtualized network function cloud 325 and/or one or more cloud computing environments 375. In various embodiments, this cloud networking architecture is an open architecture that leverages application programming interfaces (APIs); reduces complexity from services and operations; supports more nimble business models; and rapidly and seamlessly scales to meet evolving customer requirements including traffic growth, diversity of traffic types, and diversity of performance and reliability expectations.

In contrast to traditional network elements—which are typically integrated to perform a single function, the virtualized communication network employs virtual network elements (VNEs) 330, 332, 334, etc. that perform some or all of the functions of network elements 150, 152, 154, 156, etc. For example, the network architecture can provide a substrate of networking capability, often called Network Function Virtualization Infrastructure (NFVI) or simply infrastructure that is capable of being directed with software and Software Defined Networking (SDN) protocols to perform a broad variety of network functions and services. This infrastructure can include several types of substrates. The most typical type of substrate being servers that support Network Function Virtualization (NFV), followed by packet forwarding capabilities based on generic computing resources, with specialized network technologies brought to bear when general purpose processors or general purpose integrated circuit devices offered by merchants (referred to herein as merchant silicon) are not appropriate. In this case, communication services can be implemented as cloud-centric workloads.

As an example, a traditional network element 150 (shown in FIG. 1), such as an edge router can be implemented via a VNE 330 composed of NFV software modules, merchant silicon, and associated controllers. The software can be written so that increasing workload consumes incremental resources from a common resource pool, and moreover so that it's elastic: so the resources are only consumed when needed. In a similar fashion, other network elements such as other routers, switches, edge caches, and middle-boxes are instantiated from the common resource pool. Such sharing of infrastructure across a broad set of uses makes planning and growing infrastructure easier to manage.

In an embodiment, the transport layer 350 includes fiber, cable, wired and/or wireless transport elements, network elements and interfaces to provide broadband access 110, wireless access 120, voice access 130, media access 140 and/or access to content sources 175 for distribution of content to any or all of the access technologies. In particular, in some cases a network element needs to be positioned at a specific place, and this allows for less sharing of common infrastructure. Other times, the network elements have specific physical layer adapters that cannot be abstracted or virtualized and might require special DSP code and analog front-ends (AFEs) that do not lend themselves to implementation as VNEs 330, 332 or 334. These network elements can be included in transport layer 350.

The virtualized network function cloud 325 interfaces with the transport layer 350 to provide the VNEs 330, 332, 334, etc. to provide specific NFVs. In particular, the virtualized network function cloud 325 leverages cloud operations, applications, and architectures to support networking workloads. The virtualized network elements 330, 332 and 334 can employ network function software that provides either a one-for-one mapping of traditional network element function or alternately some combination of network functions designed for cloud computing. For example, VNEs 330, 332 and 334 can include route reflectors, domain name system (DNS) servers, and dynamic host configuration protocol (DHCP) servers, system architecture evolution (SAE) and/or mobility management entity (MME) gateways, broadband network gateways, IP edge routers for IP-VPN, Ethernet and other services, load balancers, distributers and other network elements. Because these elements don't typically need to forward large amounts of traffic, their workload can be distributed across a number of servers—each of which adds a portion of the capability, and overall which creates an elastic function with higher availability than its former monolithic version. These virtual network elements 330, 332, 334, etc. can be instantiated and managed using an orchestration approach similar to those used in cloud compute services.

The cloud computing environments 375 can interface with the virtualized network function cloud 325 via APIs that expose functional capabilities of the VNEs 330, 332, 334, etc. to provide the flexible and expanded capabilities to the virtualized network function cloud 325. In particular, network workloads may have applications distributed across the virtualized network function cloud 325 and cloud computing environment 375 and in the commercial cloud or might simply orchestrate workloads supported entirely in NFV infrastructure from these third party locations.

Turning now to FIG. 4, there is illustrated a block diagram of a computing environment in accordance with various aspects described herein. In order to provide additional context for various embodiments of the embodiments described herein, FIG. 4 and the following discussion are intended to provide a brief, general description of a suitable computing environment 400 in which the various embodiments of the subject disclosure can be implemented. In particular, computing environment 400 can be used in the implementation of network elements 150, 152, 154, 156, access terminal 112, base station or access point 122, switching device 132, media terminal 142, and/or VNEs 330, 332, 334, etc. Each of these devices can be implemented via computer-executable instructions that can run on one or more computers, and/or in combination with other program modules and/or as a combination of hardware and software. For example, computing environment 400 can facilitate, in whole or in part, providing a Monte Carlo simulation via a microservice. A request for a Monte Carlo simulation of a dynamic system can be received. A request for quantile samples for variables of the dynamic system can be sent to database server. A reduce-size set of quantile samples can be received from the database server over a network. A standard set of M quantile samples, which divides the variables into 1/M probability steps, can be converted to a reduced sized set of N quantile samples, which divide the variables into 1/N probability steps. By sending a reduced size set of quantile samples from the database server the network demands are decreased, and the speed is increased. Interpolation can be performed on the reduced size set of quantile samples to generate a restored size set of quantile samples. The Monte Carlo simulation can be performed on the restored size set of quantile samples and the results can be reported to a requesting client device.

Generally, program modules comprise routines, programs, components, data structures, etc., that perform particular tasks or implement particular abstract data types. Moreover, those skilled in the art will appreciate that the methods can be practiced with other computer system configurations, comprising single-processor or multiprocessor computer systems, minicomputers, mainframe computers, as well as personal computers, hand-held computing devices, microprocessor-based or programmable consumer electronics, and the like, each of which can be operatively coupled to one or more associated devices.

As used herein, a processing circuit includes one or more processors as well as other application specific circuits such as an application specific integrated circuit, digital logic circuit, state machine, programmable gate array or other circuit that processes input signals or data and that produces output signals or data in response thereto. It should be noted that while any functions and features described herein in association with the operation of a processor could likewise be performed by a processing circuit.

The illustrated embodiments of the embodiments herein can be also practiced in distributed computing environments where certain tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules can be located in both local and remote memory storage devices.

Computing devices typically comprise a variety of media, which can comprise computer-readable storage media and/or communications media, which two terms are used herein differently from one another as follows. Computer-readable storage media can be any available storage media that can be accessed by the computer and comprises both volatile and nonvolatile media, removable and non-removable media. By way of example, and not limitation, computer-readable storage media can be implemented in connection with any method or technology for storage of information such as computer-readable instructions, program modules, structured data or unstructured data.

Computer-readable storage media can comprise, but are not limited to, random access memory (RAM), read only memory (ROM), electrically erasable programmable read only memory (EEPROM), flash memory or other memory technology, compact disk read only memory (CD-ROM), digital versatile disk (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices or other tangible and/or non-transitory media which can be used to store desired information. In this regard, the terms “tangible” or “non-transitory” herein as applied to storage, memory or computer-readable media, are to be understood to exclude only propagating transitory signals per se as modifiers and do not relinquish rights to all standard storage, memory or computer-readable media that are not only propagating transitory signals per se.

Computer-readable storage media can be accessed by one or more local or remote computing devices, e.g., via access requests, queries or other data retrieval protocols, for a variety of operations with respect to the information stored by the medium.

Communications media typically embody computer-readable instructions, data structures, program modules or other structured or unstructured data in a data signal such as a modulated data signal, e.g., a carrier wave or other transport mechanism, and comprises any information delivery or transport media. The term “modulated data signal” or signals refers to a signal that has one or more of its characteristics set or changed in such a manner as to encode information in one or more signals. By way of example, and not limitation, communication media comprise wired media, such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared and other wireless media.

With reference again to FIG. 4, the example environment can comprise a computer 402, the computer 402 comprising a processing unit 404, a system memory 406 and a system bus 408. The system bus 408 couples system components including, but not limited to, the system memory 406 to the processing unit 404. The processing unit 404 can be any of various commercially available processors. Dual microprocessors and other multiprocessor architectures can also be employed as the processing unit 404.

The system bus 408 can be any of several types of bus structure that can further interconnect to a memory bus (with or without a memory controller), a peripheral bus, and a local bus using any of a variety of commercially available bus architectures. The system memory 406 comprises ROM 410 and RAM 412. A basic input/output system (BIOS) can be stored in a non-volatile memory such as ROM, erasable programmable read only memory (EPROM), EEPROM, which BIOS contains the basic routines that help to transfer information between elements within the computer 402, such as during startup. The RAM 412 can also comprise a high-speed RAM such as static RAM for caching data.

The computer 402 further comprises an internal hard disk drive (HDD) 414 (e.g., EIDE, SATA), which internal HDD 414 can also be configured for external use in a suitable chassis (not shown), a magnetic floppy disk drive (FDD) 416, (e.g., to read from or write to a removable diskette 418) and an optical disk drive 420, (e.g., reading a CD-ROM disk 422 or, to read from or write to other high capacity optical media such as the DVD). The HDD 414, magnetic FDD 416 and optical disk drive 420 can be connected to the system bus 408 by a hard disk drive interface 424, a magnetic disk drive interface 426 and an optical drive interface 428, respectively. The hard disk drive interface 424 for external drive implementations comprises at least one or both of Universal Serial Bus (USB) and Institute of Electrical and Electronics Engineers (IEEE) 1394 interface technologies. Other external drive connection technologies are within contemplation of the embodiments described herein.

The drives and their associated computer-readable storage media provide nonvolatile storage of data, data structures, computer-executable instructions, and so forth. For the computer 402, the drives and storage media accommodate the storage of any data in a suitable digital format. Although the description of computer-readable storage media above refers to a hard disk drive (HDD), a removable magnetic diskette, and a removable optical media such as a CD or DVD, it should be appreciated by those skilled in the art that other types of storage media which are readable by a computer, such as zip drives, magnetic cassettes, flash memory cards, cartridges, and the like, can also be used in the example operating environment, and further, that any such storage media can contain computer-executable instructions for performing the methods described herein.

A number of program modules can be stored in the drives and RAM 412, comprising an operating system 430, one or more application programs 432, other program modules 434 and program data 436. All or portions of the operating system, applications, modules, and/or data can also be cached in the RAM 412. The systems and methods described herein can be implemented utilizing various commercially available operating systems or combinations of operating systems.

A user can enter commands and information into the computer 402 through one or more wired/wireless input devices, e.g., a keyboard 438 and a pointing device, such as a mouse 440. Other input devices (not shown) can comprise a microphone, an infrared (IR) remote control, a joystick, a game pad, a stylus pen, touch screen or the like. These and other input devices are often connected to the processing unit 404 through an input device interface 442 that can be coupled to the system bus 408, but can be connected by other interfaces, such as a parallel port, an IEEE 1394 serial port, a game port, a universal serial bus (USB) port, an IR interface, etc.

A monitor 444 or other type of display device can be also connected to the system bus 408 via an interface, such as a video adapter 446. It will also be appreciated that in alternative embodiments, a monitor 444 can also be any display device (e.g., another computer having a display, a smart phone, a tablet computer, etc.) for receiving display information associated with computer 402 via any communication means, including via the Internet and cloud-based networks. In addition to the monitor 444, a computer typically comprises other peripheral output devices (not shown), such as speakers, printers, etc.

The computer 402 can operate in a networked environment using logical connections via wired and/or wireless communications to one or more remote computers, such as a remote computer(s) 448. The remote computer(s) 448 can be a workstation, a server computer, a router, a personal computer, portable computer, microprocessor-based entertainment appliance, a peer device or other common network node, and typically comprises many or all of the elements described relative to the computer 402, although, for purposes of brevity, only a remote memory/storage device 450 is illustrated. The logical connections depicted comprise wired/wireless connectivity to a local area network (LAN) 452 and/or larger networks, e.g., a wide area network (WAN) 454. Such LAN and WAN networking environments are commonplace in offices and companies, and facilitate enterprise-wide computer networks, such as intranets, all of which can connect to a global communications network, e.g., the Internet.

When used in a LAN networking environment, the computer 402 can be connected to the LAN 452 through a wired and/or wireless communication network interface or adapter 456. The adapter 456 can facilitate wired or wireless communication to the LAN 452, which can also comprise a wireless AP disposed thereon for communicating with the adapter 456.

When used in a WAN networking environment, the computer 402 can comprise a modem 458 or can be connected to a communications server on the WAN 454 or has other means for establishing communications over the WAN 454, such as by way of the Internet. The modem 458, which can be internal or external and a wired or wireless device, can be connected to the system bus 408 via the input device interface 442. In a networked environment, program modules depicted relative to the computer 402 or portions thereof, can be stored in the remote memory/storage device 450. It will be appreciated that the network connections shown are example and other means of establishing a communications link between the computers can be used.

The computer 402 can be operable to communicate with any wireless devices or entities operatively disposed in wireless communication, e.g., a printer, scanner, desktop and/or portable computer, portable data assistant, communications satellite, any piece of equipment or location associated with a wirelessly detectable tag (e.g., a kiosk, news stand, restroom), and telephone. This can comprise Wireless Fidelity (Wi-Fi) and BLUETOOTH® wireless technologies. Thus, the communication can be a predefined structure as with a conventional network or simply an ad hoc communication between at least two devices.

Wi-Fi can allow connection to the Internet from a couch at home, a bed in a hotel room or a conference room at work, without wires. Wi-Fi is a wireless technology similar to that used in a cell phone that enables such devices, e.g., computers, to send and receive data indoors and out; anywhere within the range of a base station. Wi-Fi networks use radio technologies called IEEE 802.11 (a, b, g, n, ac, ag, etc.) to provide secure, reliable, fast wireless connectivity. A Wi-Fi network can be used to connect computers to each other, to the Internet, and to wired networks (which can use IEEE 802.3 or Ethernet). Wi-Fi networks operate in the unlicensed 2.4 and 5 GHz radio bands for example or with products that contain both bands (dual band), so the networks can provide real-world performance similar to the basic 10BaseT wired Ethernet networks used in many offices.

Turning now to FIG. 5, an embodiment 500 of a mobile network platform 510 is shown that is an example of network elements 150, 152, 154, 156, and/or VNEs 330, 332, 334, etc. For example, platform 510 can facilitate, in whole or in part, providing a Monte Carlo simulation via a microservice. A request for a Monte Carlo simulation of a dynamic system can be received. A request for quantile samples for variables of the dynamic system can be sent to database server. A reduce-size set of quantile samples can be received from the database server over a network. A standard set of M quantile samples, which divides the variables into 1/M probability steps, can be converted to a reduced sized set of N quantile samples, which divide the variables into 1/N probability steps. By sending a reduced size set of quantile samples from the database server the network demands are decreased, and the speed is increased. Interpolation can be performed on the reduced size set of quantile samples to generate a restored size set of quantile samples. The Monte Carlo simulation can be performed on the restored size set of quantile samples and the results can be reported to a requesting client device.

In one or more embodiments, the mobile network platform 510 can generate and receive signals transmitted and received by base stations or access points such as base station or access point 122. Generally, mobile network platform 510 can comprise components, e.g., nodes, gateways, interfaces, servers, or disparate platforms, that facilitate both packet-switched (PS) (e.g., internet protocol (IP), frame relay, asynchronous transfer mode (ATM)) and circuit-switched (CS) traffic (e.g., voice and data), as well as control generation for networked wireless telecommunication. As a non-limiting example, mobile network platform 510 can be included in telecommunications carrier networks and can be considered carrier-side components as discussed elsewhere herein. Mobile network platform 510 comprises CS gateway node(s) 512 which can interface CS traffic received from legacy networks like telephony network(s) 540 (e.g., public switched telephone network (PSTN), or public land mobile network (PLMN)) or a signaling system #7 (SS7) network 560. CS gateway node(s) 512 can authorize and authenticate traffic (e.g., voice) arising from such networks. Additionally, CS gateway node(s) 512 can access mobility, or roaming, data generated through SS7 network 560; for instance, mobility data stored in a visited location register (VLR), which can reside in memory 530. Moreover, CS gateway node(s) 512 interfaces CS-based traffic and signaling and PS gateway node(s) 518. As an example, in a 3GPP UMTS network, CS gateway node(s) 512 can be realized at least in part in gateway GPRS support node(s) (GGSN). It should be appreciated that functionality and specific operation of CS gateway node(s) 512, PS gateway node(s) 518, and serving node(s) 516, is provided and dictated by radio technology(ies) utilized by mobile network platform 510 for telecommunication over a radio access network 520 with other devices, such as a radiotelephone 575.

In addition to receiving and processing CS-switched traffic and signaling, PS gateway node(s) 518 can authorize and authenticate PS-based data sessions with served mobile devices. Data sessions can comprise traffic, or content(s), exchanged with networks external to the mobile network platform 510, like wide area network(s) (WANs) 550, enterprise network(s) 570, and service network(s) 580, which can be embodied in local area network(s) (LANs), can also be interfaced with mobile network platform 510 through PS gateway node(s) 518. It is to be noted that WANs 550 and enterprise network(s) 570 can embody, at least in part, a service network(s) like IP multimedia subsystem (IMS). Based on radio technology layer(s) available in technology resource(s) or radio access network 520, PS gateway node(s) 518 can generate packet data protocol contexts when a data session is established; other data structures that facilitate routing of packetized data also can be generated. To that end, in an aspect, PS gateway node(s) 518 can comprise a tunnel interface (e.g., tunnel termination gateway (TTG) in 3GPP UMTS network(s) (not shown)) which can facilitate packetized communication with disparate wireless network(s), such as Wi-Fi networks.

In embodiment 500, mobile network platform 510 also comprises serving node(s) 516 that, based upon available radio technology layer(s) within technology resource(s) in the radio access network 520, convey the various packetized flows of data streams received through PS gateway node(s) 518. It is to be noted that for technology resource(s) that rely primarily on CS communication, server node(s) can deliver traffic without reliance on PS gateway node(s) 518; for example, server node(s) can embody at least in part a mobile switching center. As an example, in a 3GPP UMTS network, serving node(s) 516 can be embodied in serving GPRS support node(s) (SGSN).

For radio technologies that exploit packetized communication, server(s) 514 in mobile network platform 510 can execute numerous applications that can generate multiple disparate packetized data streams or flows, and manage (e.g., schedule, queue, format . . . ) such flows. Such application(s) can comprise add-on features to standard services (for example, provisioning, billing, customer support . . . ) provided by mobile network platform 510. Data streams (e.g., content(s) that are part of a voice call or data session) can be conveyed to PS gateway node(s) 518 for authorization/authentication and initiation of a data session, and to serving node(s) 516 for communication thereafter. In addition to application server, server(s) 514 can comprise utility server(s), a utility server can comprise a provisioning server, an operations and maintenance server, a security server that can implement at least in part a certificate authority and firewalls as well as other security mechanisms, and the like. In an aspect, security server(s) secure communication served through mobile network platform 510 to ensure network's operation and data integrity in addition to authorization and authentication procedures that CS gateway node(s) 512 and PS gateway node(s) 518 can enact. Moreover, provisioning server(s) can provision services from external network(s) like networks operated by a disparate service provider; for instance, WAN 550 or Global Positioning System (GPS) network(s) (not shown). Provisioning server(s) can also provision coverage through networks associated to mobile network platform 510 (e.g., deployed and operated by the same service provider), such as the distributed antennas networks shown in FIG. 1(s) that enhance wireless service coverage by providing more network coverage.

It is to be noted that server(s) 514 can comprise one or more processors configured to confer at least in part the functionality of mobile network platform 510. To that end, the one or more processor can execute code instructions stored in memory 530, for example. It is should be appreciated that server(s) 514 can comprise a content manager, which operates in substantially the same manner as described hereinbefore.

In example embodiment 500, memory 530 can store information related to operation of mobile network platform 510. Other operational information can comprise provisioning information of mobile devices served through mobile network platform 510, subscriber databases; application intelligence, pricing schemes, e.g., promotional rates, flat-rate programs, couponing campaigns; technical specification(s) consistent with telecommunication protocols for operation of disparate radio, or wireless, technology layers; and so forth. Memory 530 can also store information from at least one of telephony network(s) 540, WAN 550, SS7 network 560, or enterprise network(s) 570. In an aspect, memory 530 can be, for example, accessed as part of a data store component or as a remotely connected memory store.

In order to provide a context for the various aspects of the disclosed subject matter, FIG. 5, and the following discussion, are intended to provide a brief, general description of a suitable environment in which the various aspects of the disclosed subject matter can be implemented. While the subject matter has been described above in the general context of computer-executable instructions of a computer program that runs on a computer and/or computers, those skilled in the art will recognize that the disclosed subject matter also can be implemented in combination with other program modules. Generally, program modules comprise routines, programs, components, data structures, etc. that perform particular tasks and/or implement particular abstract data types.

Turning now to FIG. 6, an illustrative embodiment of a communication device 600 is shown. The communication device 600 can serve as an illustrative embodiment of devices such as data terminals 114, mobile devices 124, vehicle 126, display devices 144 or other client devices for communication via either communications network 125. For example, computing device 600 can facilitate, in whole or in part, providing a Monte Carlo simulation via a microservice. A request for a Monte Carlo simulation of a dynamic system can be received. A request for quantile samples for variables of the dynamic system can be sent to database server. A reduce-size set of quantile samples can be received from the database server over a network. A standard set of M quantile samples, which divides the variables into 1/M probability steps, can be converted to a reduced sized set of N quantile samples, which divide the variables into 1/N probability steps. By sending a reduced size set of quantile samples from the database server the network demands are decreased, and the speed is increased. Interpolation can be performed on the reduced size set of quantile samples to generate a restored size set of quantile samples. The Monte Carlo simulation can be performed on the restored size set of quantile samples and the results can be reported to a requesting client device.

The communication device 600 can comprise a wireline and/or wireless transceiver 602 (herein transceiver 602), a user interface (UI) 604, a power supply 614, a location receiver 616, a motion sensor 618, an orientation sensor 620, and a controller 606 for managing operations thereof. The transceiver 602 can support short-range or long-range wireless access technologies such as Bluetooth®, ZigBee®, WiFi, DECT, or cellular communication technologies, just to mention a few (Bluetooth® and ZigBee® are trademarks registered by the Bluetooth® Special Interest Group and the ZigBee® Alliance, respectively). Cellular technologies can include, for example, CDMA-1X, UMTS/HSDPA, GSM/GPRS, TDMA/EDGE, EV/DO, WiMAX, SDR, LTE, as well as other next generation wireless communication technologies as they arise. The transceiver 602 can also be adapted to support circuit-switched wireline access technologies (such as PSTN), packet-switched wireline access technologies (such as TCP/IP, VoIP, etc.), and combinations thereof.

The UI 604 can include a depressible or touch-sensitive keypad 608 with a navigation mechanism such as a roller ball, a joystick, a mouse, or a navigation disk for manipulating operations of the communication device 600. The keypad 608 can be an integral part of a housing assembly of the communication device 600 or an independent device operably coupled thereto by a tethered wireline interface (such as a USB cable) or a wireless interface supporting for example Bluetooth®. The keypad 608 can represent a numeric keypad commonly used by phones, and/or a QWERTY keypad with alphanumeric keys. The UI 604 can further include a display 610 such as monochrome or color LCD (Liquid Crystal Display), OLED (Organic Light Emitting Diode) or other suitable display technology for conveying images to an end user of the communication device 600. In an embodiment where the display 610 is touch-sensitive, a portion or all of the keypad 608 can be presented by way of the display 610 with navigation features.

The display 610 can use touch screen technology to also serve as a user interface for detecting user input. As a touch screen display, the communication device 600 can be adapted to present a user interface having graphical user interface (GUI) elements that can be selected by a user with a touch of a finger. The display 610 can be equipped with capacitive, resistive or other forms of sensing technology to detect how much surface area of a user's finger has been placed on a portion of the touch screen display. This sensing information can be used to control the manipulation of the GUI elements or other functions of the user interface. The display 610 can be an integral part of the housing assembly of the communication device 600 or an independent device communicatively coupled thereto by a tethered wireline interface (such as a cable) or a wireless interface.

The UI 604 can also include an audio system 612 that utilizes audio technology for conveying low volume audio (such as audio heard in proximity of a human ear) and high volume audio (such as speakerphone for hands free operation). The audio system 612 can further include a microphone for receiving audible signals of an end user. The audio system 612 can also be used for voice recognition applications. The UI 604 can further include an image sensor 613 such as a charged coupled device (CCD) camera for capturing still or moving images.

The power supply 614 can utilize common power management technologies such as replaceable and rechargeable batteries, supply regulation technologies, and/or charging system technologies for supplying energy to the components of the communication device 600 to facilitate long-range or short-range portable communications. Alternatively, or in combination, the charging system can utilize external power sources such as DC power supplied over a physical interface such as a USB port or other suitable tethering technologies.

The location receiver 616 can utilize location technology such as a global positioning system (GPS) receiver capable of assisted GPS for identifying a location of the communication device 600 based on signals generated by a constellation of GPS satellites, which can be used for facilitating location services such as navigation. The motion sensor 618 can utilize motion sensing technology such as an accelerometer, a gyroscope, or other suitable motion sensing technology to detect motion of the communication device 600 in three-dimensional space. The orientation sensor 620 can utilize orientation sensing technology such as a magnetometer to detect the orientation of the communication device 600 (north, south, west, and east, as well as combined orientations in degrees, minutes, or other suitable orientation metrics).

The communication device 600 can use the transceiver 602 to also determine a proximity to a cellular, WiFi, Bluetooth®, or other wireless access points by sensing techniques such as utilizing a received signal strength indicator (RSSI) and/or signal time of arrival (TOA) or time of flight (TOF) measurements. The controller 606 can utilize computing technologies such as a microprocessor, a digital signal processor (DSP), programmable gate arrays, application specific integrated circuits, and/or a video processor with associated storage memory such as Flash, ROM, RAM, SRAM, DRAM or other storage technologies for executing computer instructions, controlling, and processing data supplied by the aforementioned components of the communication device 600.

Other components not shown in FIG. 6 can be used in one or more embodiments of the subject disclosure. For instance, the communication device 600 can include a slot for adding or removing an identity module such as a Subscriber Identity Module (SIM) card or Universal Integrated Circuit Card (UICC). SIM or UICC cards can be used for identifying subscriber services, executing programs, storing subscriber data, and so on.

The terms “first,” “second,” “third,” and so forth, as used in the claims, unless otherwise clear by context, is for clarity only and doesn't otherwise indicate or imply any order in time. For instance, “a first determination,” “a second determination,” and “a third determination,” does not indicate or imply that the first determination is to be made before the second determination, or vice versa, etc.

In the subject specification, terms such as “store,” “storage,” “data store,” data storage,” “database,” and substantially any other information storage component relevant to operation and functionality of a component, refer to “memory components,” or entities embodied in a “memory” or components comprising the memory. It will be appreciated that the memory components described herein can be either volatile memory or nonvolatile memory, or can comprise both volatile and nonvolatile memory, by way of illustration, and not limitation, volatile memory, non-volatile memory, disk storage, and memory storage. Further, nonvolatile memory can be included in read only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable ROM (EEPROM), or flash memory. Volatile memory can comprise random access memory (RAM), which acts as external cache memory. By way of illustration and not limitation, RAM is available in many forms such as synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), and direct Rambus RAM (DRRAM). Additionally, the disclosed memory components of systems or methods herein are intended to comprise, without being limited to comprising, these and any other suitable types of memory.

Moreover, it will be noted that the disclosed subject matter can be practiced with other computer system configurations, comprising single-processor or multiprocessor computer systems, mini-computing devices, mainframe computers, as well as personal computers, hand-held computing devices (e.g., PDA, phone, smartphone, watch, tablet computers, netbook computers, etc.), microprocessor-based or programmable consumer or industrial electronics, and the like. The illustrated aspects can also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network; however, some if not all aspects of the subject disclosure can be practiced on stand-alone computers. In a distributed computing environment, program modules can be located in both local and remote memory storage devices.

In one or more embodiments, information regarding use of services can be generated including services being accessed, media consumption history, user preferences, and so forth. This information can be obtained by various methods including user input, detecting types of communications (e.g., video content vs. audio content), analysis of content streams, sampling, and so forth. The generating, obtaining and/or monitoring of this information can be responsive to an authorization provided by the user. In one or more embodiments, an analysis of data can be subject to authorization from user(s) associated with the data, such as an opt-in, an opt-out, acknowledgement requirements, notifications, selective authorization based on types of data, and so forth.

Some of the embodiments described herein can also employ artificial intelligence (AI) to facilitate automating one or more features described herein. The embodiments (e.g., in connection with automatically identifying acquired cell sites that provide a maximum value/benefit after addition to an existing communication network) can employ various AI-based schemes for carrying out various embodiments thereof. Moreover, the classifier can be employed to determine a ranking or priority of each cell site of the acquired network. A classifier is a function that maps an input attribute vector, x=(x1, x2, x3, x4, . . . , xn), to a confidence that the input belongs to a class, that is, f(x)=confidence (class). Such classification can employ a probabilistic and/or statistical-based analysis (e.g., factoring into the analysis utilities and costs) to determine or infer an action that a user desires to be automatically performed. A support vector machine (SVM) is an example of a classifier that can be employed. The SVM operates by finding a hypersurface in the space of possible inputs, which the hypersurface attempts to split the triggering criteria from the non-triggering events. Intuitively, this makes the classification correct for testing data that is near, but not identical to training data. Other directed and undirected model classification approaches comprise, e.g., naïve Bayes, Bayesian networks, decision trees, neural networks, fuzzy logic models, and probabilistic classification models providing different patterns of independence can be employed. Classification as used herein also is inclusive of statistical regression that is utilized to develop models of priority.

As will be readily appreciated, one or more of the embodiments can employ classifiers that are explicitly trained (e.g., via a generic training data) as well as implicitly trained (e.g., via observing UE behavior, operator preferences, historical information, receiving extrinsic information). For example, SVMs can be configured via a learning or training phase within a classifier constructor and feature selection module. Thus, the classifier(s) can be used to automatically learn and perform a number of functions, including but not limited to determining according to predetermined criteria which of the acquired cell sites will benefit a maximum number of subscribers and/or which of the acquired cell sites will add minimum value to the existing communication network coverage, etc.

As used in some contexts in this application, in some embodiments, the terms “component,” “system” and the like are intended to refer to, or comprise, a computer-related entity or an entity related to an operational apparatus with one or more specific functionalities, wherein the entity can be either hardware, a combination of hardware and software, software, or software in execution. As an example, a component may be, but is not limited to being, a process running on a processor, a processor, an object, an executable, a thread of execution, computer-executable instructions, a program, and/or a computer. By way of illustration and not limitation, both an application running on a server and the server can be a component. One or more components may reside within a process and/or thread of execution and a component may be localized on one computer and/or distributed between two or more computers. In addition, these components can execute from various computer readable media having various data structures stored thereon. The components may communicate via local and/or remote processes such as in accordance with a signal having one or more data packets (e.g., data from one component interacting with another component in a local system, distributed system, and/or across a network such as the Internet with other systems via the signal). As another example, a component can be an apparatus with specific functionality provided by mechanical parts operated by electric or electronic circuitry, which is operated by a software or firmware application executed by a processor, wherein the processor can be internal or external to the apparatus and executes at least a part of the software or firmware application. As yet another example, a component can be an apparatus that provides specific functionality through electronic components without mechanical parts, the electronic components can comprise a processor therein to execute software or firmware that confers at least in part the functionality of the electronic components. While various components have been illustrated as separate components, it will be appreciated that multiple components can be implemented as a single component, or a single component can be implemented as multiple components, without departing from example embodiments.

Further, the various embodiments can be implemented as a method, apparatus or article of manufacture using standard programming and/or engineering techniques to produce software, firmware, hardware or any combination thereof to control a computer to implement the disclosed subject matter. The term “article of manufacture” as used herein is intended to encompass a computer program accessible from any computer-readable device or computer-readable storage/communications media. For example, computer readable storage media can include, but are not limited to, magnetic storage devices (e.g., hard disk, floppy disk, magnetic strips), optical disks (e.g., compact disk (CD), digital versatile disk (DVD)), smart cards, and flash memory devices (e.g., card, stick, key drive). Of course, those skilled in the art will recognize many modifications can be made to this configuration without departing from the scope or spirit of the various embodiments.

In addition, the words “example” and “exemplary” are used herein to mean serving as an instance or illustration. Any embodiment or design described herein as “example” or “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments or designs. Rather, use of the word example or exemplary is intended to present concepts in a concrete fashion. As used in this application, the term “or” is intended to mean an inclusive “or” rather than an exclusive “or”. That is, unless specified otherwise or clear from context, “X employs A or B” is intended to mean any of the natural inclusive permutations. That is, if X employs A; X employs B; or X employs both A and B, then “X employs A or B” is satisfied under any of the foregoing instances. In addition, the articles “a” and “an” as used in this application and the appended claims should generally be construed to mean “one or more” unless specified otherwise or clear from context to be directed to a singular form.

Moreover, terms such as “user equipment,” “mobile station,” “mobile,” subscriber station,” “access terminal,” “terminal,” “handset,” “mobile device” (and/or terms representing similar terminology) can refer to a wireless device utilized by a subscriber or user of a wireless communication service to receive or convey data, control, voice, video, sound, gaming or substantially any data-stream or signaling-stream. The foregoing terms are utilized interchangeably herein and with reference to the related drawings.

Furthermore, the terms “user,” “subscriber,” “customer,” “consumer” and the like are employed interchangeably throughout, unless context warrants particular distinctions among the terms. It should be appreciated that such terms can refer to human entities or automated components supported through artificial intelligence (e.g., a capacity to make inference based, at least, on complex mathematical formalisms), which can provide simulated vision, sound recognition and so forth.

As employed herein, the term “processor” can refer to substantially any computing processing unit or device comprising, but not limited to comprising, single-core processors; single-processors with software multithread execution capability; multi-core processors; multi-core processors with software multithread execution capability; multi-core processors with hardware multithread technology; parallel platforms; and parallel platforms with distributed shared memory. Additionally, a processor can refer to an integrated circuit, an application specific integrated circuit (ASIC), a digital signal processor (DSP), a field programmable gate array (FPGA), a programmable logic controller (PLC), a complex programmable logic device (CPLD), a discrete gate or transistor logic, discrete hardware components or any combination thereof designed to perform the functions described herein. Processors can exploit nano-scale architectures such as, but not limited to, molecular and quantum-dot based transistors, switches and gates, in order to optimize space usage or enhance performance of user equipment. A processor can also be implemented as a combination of computing processing units.

As used herein, terms such as “data storage,” data storage,” “database,” and substantially any other information storage component relevant to operation and functionality of a component, refer to “memory components,” or entities embodied in a “memory” or components comprising the memory. It will be appreciated that the memory components or computer-readable storage media, described herein can be either volatile memory or nonvolatile memory or can include both volatile and nonvolatile memory.

What has been described above includes mere examples of various embodiments. It is, of course, not possible to describe every conceivable combination of components or methodologies for purposes of describing these examples, but one of ordinary skill in the art can recognize that many further combinations and permutations of the present embodiments are possible. Accordingly, the embodiments disclosed and/or claimed herein are intended to embrace all such alterations, modifications and variations that fall within the spirit and scope of the appended claims. Furthermore, to the extent that the term “includes” is used in either the detailed description or the claims, such term is intended to be inclusive in a manner similar to the term “comprising” as “comprising” is interpreted when employed as a transitional word in a claim.

In addition, a flow diagram may include a “start” and/or “continue” indication. The “start” and “continue” indications reflect that the steps presented can optionally be incorporated in or otherwise used in conjunction with other routines. In this context, “start” indicates the beginning of the first step presented and may be preceded by other activities not specifically shown. Further, the “continue” indication reflects that the steps presented may be performed multiple times and/or may be succeeded by other activities not specifically shown. Further, while a flow diagram indicates a particular ordering of steps, other orderings are likewise possible provided that the principles of causality are maintained.

As may also be used herein, the term(s) “operably coupled to”, “coupled to”, and/or “coupling” includes direct coupling between items and/or indirect coupling between items via one or more intervening items. Such items and intervening items include, but are not limited to, junctions, communication paths, components, circuit elements, circuits, functional blocks, and/or devices. As an example of indirect coupling, a signal conveyed from a first item to a second item may be modified by one or more intervening items by modifying the form, nature or format of information in a signal, while one or more elements of the information in the signal are nevertheless conveyed in a manner than can be recognized by the second item. In a further example of indirect coupling, an action in a first item can cause a reaction on the second item, as a result of actions and/or reactions in one or more intervening items.

Although specific embodiments have been illustrated and described herein, it should be appreciated that any arrangement which achieves the same or similar purpose may be substituted for the embodiments described or shown by the subject disclosure. The subject disclosure is intended to cover any and all adaptations or variations of various embodiments. Combinations of the above embodiments, and other embodiments not specifically described herein, can be used in the subject disclosure. For instance, one or more features from one or more embodiments can be combined with one or more features of one or more other embodiments. In one or more embodiments, features that are positively recited can also be negatively recited and excluded from the embodiment with or without replacement by another structural and/or functional feature. The steps or functions described with respect to the embodiments of the subject disclosure can be performed in any order. The steps or functions described with respect to the embodiments of the subject disclosure can be performed alone or in combination with other steps or functions of the subject disclosure, as well as from other embodiments or from other steps that have not been described in the subject disclosure. Further, more than or less than all of the features described with respect to an embodiment can also be utilized. 

What is claimed is:
 1. A method, comprising: receiving, by a processing system including a processor, a first request from a client device for a Monte Carlo simulation of a dynamic system; transmitting, by the processing system, via a network, a second request to a database server for quantile samples of a plurality of variables associated with the dynamic system responsive to the receiving the first request; receiving, by the processing system, from the database server via the network, a reduced size set of quantile samples of the plurality of variables associated with the dynamic system, wherein the reduced size set of quantile samples of the plurality of variables is based on a standard set of quantile samples of the plurality of variables associated with the dynamic system, wherein the standard set of quantile samples comprises M quantile samples based on dividing each distribution of the plurality of variables into 1/M probability steps, wherein the reduced size set of quantile samples comprises N quantile samples based on dividing each distribution of the plurality of variables into 1/N probability steps, wherein a third set of quantile samples of a first variable of the plurality of variables is added to the reduced size set of quantile samples according to the first variable being unbounded; performing, by the processing system, a plurality of linear interpolations upon the reduced size set of quantile samples of the plurality of variables associated with the dynamic system to generate a restored size set of quantile samples of the plurality of variables associated with the dynamic system; performing, by the processing system, the Monte Carlo simulation using the restored size set of quantile samples of the plurality of variables associated with the dynamic system to generate a simulation result; and transmitting, by the processing system, the simulation result to the client device.
 2. The method of claim 1, wherein the first variable of the plurality of variables is minimum unbounded, and wherein the third set of quantile samples of the first variable of the plurality of variables comprises E1 quantile samples based on dividing a first distribution of the first variable near a minimum boundary into E1 quantile samples of 1/M probability steps.
 3. The method of claim 2, wherein the third set of quantile samples of the first variable of the plurality of variables is added to the reduced size set of quantile samples of the plurality of variables after a first quantile sample of the reduced sized set of quantile samples.
 4. The method of claim 1, wherein a fourth set of quantile samples of a second variable of the plurality of variables is added to the first set of quantile samples according to the second variable being maximum unbounded.
 5. The method of claim 4, wherein the fourth set of quantile samples of the second variable of the plurality of variables comprises E2 quantile samples based on dividing a second distribution of the second variable of the plurality of variables near a maximum boundary into E1 quantile samples of 1/M probability steps.
 6. The method of claim 4, wherein the fourth set of quantile samples of the second variable of the plurality of variables is added to the reduced size set of quantile samples before a last quantile sample of the reduced sized set of quantile samples.
 7. The method of claim 1, wherein comprises M quantile samples based on dividing each distribution of the plurality of variables associated with the dynamic system into 1/M probability steps.
 8. The method of claim 1, wherein the reduced size set of quantile samples is stored at the database server in text format.
 9. The method of claim 1, wherein E1 and E2 are both equal to
 5. 10. The method of claim 1, wherein a ratio of M/N comprises ten.
 11. The method of claim 1, wherein the dynamic system is a telecommunication system.
 12. A device, comprising: a processing system including a processor; and a memory that stores executable instructions that, when executed by the processing system, facilitate performance of operations, the operations comprising: transmitting, via a network, a request to a database server for quantile samples of a plurality of variables associated with a dynamic system; receiving from the database server via the network, a reduced size set of quantile samples of the plurality of variables associated with the dynamic system, wherein the reduced size set of quantile samples of the plurality of variables is based on a standard set of quantile samples of the plurality of variables associated with the dynamic system, wherein the standard set of quantile samples comprises M quantile samples based on dividing each distribution of the plurality of variables into 1/M probability steps, and wherein the reduced size set of quantile samples comprises N quantile samples based on dividing each distribution of the plurality of variables into 1/N probability steps; performing a plurality of linear interpolations upon the reduced size set of quantile samples of the plurality of variables associated with the dynamic system to generate a restored size set of quantile samples of the plurality of variables associated with the dynamic system; performing a Monte Carlo simulation using the restored size set of quantile samples of the plurality of variables associated with the dynamic system to generate a simulation result; and transmitting the simulation result to a client device.
 13. The device of claim 12, wherein a third set of quantile samples of a first variable of the plurality of variables is added to the reduced size set of quantile samples according to the first variable being minimum unbounded, and wherein the third set of quantile samples comprises E1 quantile samples based on dividing a first distribution of the first variable near a minimum boundary into E1 quantile samples of 1/M probability steps.
 14. The device of claim 13, wherein the third set of quantile samples of the first variable of the plurality of variables is added to the reduced size set of quantile samples after a first quantile sample of the reduced sized set of quantile samples.
 15. The device of claim 12, wherein a third set of quantile samples of a first variable of the plurality of variables is added to the first set of quantile samples of the plurality of variables according to the first variable being maximum unbounded, and wherein the third set of quantile samples comprises E2 quantile samples based on dividing a first distribution of the first variable near a maximum boundary into E1 quantile samples of 1/M probability steps.
 16. The device of claim 15, wherein the third set of quantile samples of the third variable of the plurality of variables is added to the reduced size set of quantile samples before a last quantile sample of the reduced sized set of quantile samples.
 17. The device of claim 12, wherein the restored size set of quantile samples of the plurality of variables comprises M quantile samples based on dividing each distribution of the plurality of variables associated with the dynamic system into 1/M probability steps.
 18. A non-transitory machine-readable medium, comprising executable instructions that, when executed by a processing system including a processor, facilitate performance of operations, the operations comprising: receiving from a database server via a network, a reduced size set of quantile samples of a plurality of variables associated with a dynamic system, wherein the reduced size set of quantile samples of the plurality of variables is based on a standard set of quantile samples of the plurality of variables associated with the dynamic system, wherein the standard set of quantile samples comprises M quantile samples based on dividing each distribution of the plurality of variables into 1/M probability steps, and wherein the reduced size set of quantile samples comprises N quantile samples based on dividing each distribution of the plurality of variables into 1/N probability steps; performing a plurality of linear interpolations upon the reduced size set of quantile samples of the plurality of variables associated with the dynamic system to generate a restored size set of quantile samples of the plurality of variables associated with the dynamic system; performing a Monte Carlo simulation using the restored size set of quantile samples of the plurality of variables associated with the dynamic system to generate a simulation result; and transmitting the simulation result to a client device.
 19. The non-transitory machine-readable medium of claim 18, wherein the operations further comprise transmitting, via the network, a request to the database server for quantile samples of a plurality of variables associated with a dynamic system.
 20. The non-transitory machine-readable medium of claim 18, wherein a third set of quantile samples of a first variable of the plurality of variables is added to the reduced size set of quantile samples according to the first variable being minimum unbounded, and wherein the third set of quantile samples comprises E1 quantile samples based on dividing a first distribution of the first variable near a minimum boundary into E1 quantile samples of 1/M probability steps. 